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It seems that you uploaded an image of a geometric sequence assignment. I'll extract and solve the problems for you based on the content.

From the image:

### Task:
You are asked to:
1. **Find the common ratio** of each geometric sequence.
2. **Find the next term** of the sequence.

Let's go through each sequence in detail:

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### Sequences provided:

1. **Sequence A**:  
   \( 5, 15, 45, \dots \)
   
2. **Sequence B**:  
   \( 10, 2, 0.4, \dots \)
   
3. **Sequence C**:  
   \( 625, 125, 25, \dots \)
   
4. **Sequence X**:  
   \( \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \dots \)
   
5. **Sequence Y**:  
   \( 4, -8, 16, \dots \)
   
6. **Sequence Z**:  
   \( \frac{3}{4}, \frac{9}{16}, \frac{27}{64}, \dots \)

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Now, I'll compute the **common ratio** and the **next term** for each sequence.

### 1. **Sequence A: \( 5, 15, 45, \dots \)**

- **Common ratio** \( r = \frac{15}{5} = 3 \).
- **Next term**: \( 45 \times 3 = 135 \).

### 2. **Sequence B: \( 10, 2, 0.4, \dots \)**

- **Common ratio** \( r = \frac{2}{10} = 0.2 \).
- **Next term**: \( 0.4 \times 0.2 = 0.08 \).

### 3. **Sequence C: \( 625, 125, 25, \dots \)**

- **Common ratio** \( r = \frac{125}{625} = \frac{1}{5} \).
- **Next term**: \( 25 \times \frac{1}{5} = 5 \).

### 4. **Sequence X: \( \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \dots \)**

- **Common ratio** \( r = \frac{\frac{1}{4}}{\frac{1}{2}} = \frac{1}{2} \).
- **Next term**: \( \frac{1}{8} \times \frac{1}{2} = \frac{1}{16} \).

### 5. **Sequence Y: \( 4, -8, 16, \dots \)**

- **Common ratio** \( r = \frac{-8}{4} = -2 \).
- **Next term**: \( 16 \times -2 = -32 \).

### 6. **Sequence Z: \( \frac{3}{4}, \frac{9}{16}, \frac{27}{64}, \dots \)**

- **Common ratio** \( r = \frac{\frac{9}{16}}{\frac{3}{4}} = \frac{3}{4} \times \frac{4}{3} = \frac{3}{4} \).
- **Next term**: \( \frac{27}{64} \times \frac{3}{4} = \frac{81}{256} \).

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Would you like a deeper explanation of any particular sequence?

Here are five related questions to deepen your understanding:

1. How can you determine if a sequence is geometric?
2. What are the properties of geometric sequences?
3. Can geometric sequences have negative common ratios?
4. How can you apply geometric sequences in real-world problems?
5. What is the general formula for the \(n\)-th term of a geometric sequence?

**Tip**: In geometric sequences, multiplying by the common ratio always yields the next term, so if the ratio is fractional, the terms decrease.

Find the common ratio and the next term of each geometric sequence. Write the letter that corresponds to the given terms to answer the question below.

Learn how to find the common ratio and the next term of geometric sequences. This problem involves determining the constant multiplier (common ratio) and using it to find the subsequent term in the sequence. Suitable for students in Grades 9-10.

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